Worm pumps of the kind referred to above have until now been provided with a worm gate member in the form of a circular, gear-wheel-like disk engaging the convolutions of the worm rotor in a manner similar to the engagement of the toothed wheel with the worm in a worm gear. The function of the worm gate member is to prevent the medium being pumped from rotating together with the worm rotor, which--of course--would result in no pumping effect being produced. If in such known pumps a worm rotor with constant external diameter is used, such a wheel-shaped worm gate member can obviously only come into full engagement with the convolutions in the worm rotor at a single location of the latter. The result of this is partly an incomplete blocking of the convolutions, partly a risk that lumps in the medium being pumped, e.g., large muscular chunks in a non-comminuted meat mass, can be jammed between the worm gate member and the convolutions of the worm rotor in the region, in which the peripheral edge of the worm gate member approaches said only location, at which the blockage is effective.